Problem 132 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of oxalic acid molecules in \(100 \mathrm{ml}\) of \(0.02\) N oxalic acid solution is (a) \(6.023 \times 10^{22}\) (b) \(10^{-3}\) (c) \(6.022 \times 10^{20}\) (d) none of these

Step-by-Step Solution

Answer

Option (c) \(6.022 \times 10^{20}\) is correct.

Step 1: Understand Normality

Normality (N) is a measure of concentration equivalent to the molarity for substances that can donate or accept more than one proton or hydroxide ion. For oxalic acid (a diprotic acid), the normality is twice the molarity because it can release two protons ( ext{H}^+ ions) per molecule. Therefore, if we have a 0.02 N solution of oxalic acid, the molarity ( ext{M}) will be 0.01 M.

Step 2: Calculate Moles of Oxalic Acid

To find the number of moles of oxalic acid in the solution, use the formula for moles: \[ ext{moles} = ext{Molarity} imes ext{Volume in liters}\]Substitute the values: \[ ext{moles} = 0.01 M \times 0.1 ext{ L} = 0.001 ext{ moles}\]

Step 3: Convert Moles to Number of Molecules

Use Avogadro's number to convert moles to molecules, where 1 mole is equivalent to \(6.022 \times 10^{23}\) molecules. Multiply the moles of oxalic acid by Avogadro's number:\[ ext{Number of molecules} = 0.001 ext{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 6.022 \times 10^{20} ext{ molecules}\]

Step 4: Match the Answer to Options Provided

Compare the calculated number of molecules with the options given. From options (c) is \(6.022 \times 10^{20}\), which matches our calculated result.

Key Concepts

Molarity

Molarity is a crucial concept in chemistry, which quantifies the concentration of a solute in a solution. It is defined as the number of moles of a solute present in one liter of a solution. Molarity is expressed in units of moles per liter (mol/L) and symbolized by the letter M.
To calculate molarity, you will use the formula:

• Molarity (M) = \( \frac{\text{moles of solute}}{\text{liters of solution}} \)

Consider a solution with a molarity of 0.01 M. This means there are 0.01 moles of solute in every liter of the solution.
Understanding molarity allows you to determine how concentrated a given solute is within a solution, which is essential for chemical reactions and experiments.

Moles Calculation

Calculating moles is essential for converting between mass, volume, and molecule counts in chemistry. Moles refer to the quantity of a substance that contains as many entities (atoms, molecules) as there are in 12 grams of carbon-12.
To calculate the number of moles, use this handy formula:

• Moles = \( \text{Molarity} \times \text{Volume in liters} \)

For example, if you have a solution with a molarity of 0.01 M and a volume of 100 ml (which is 0.1 liters), the moles of solute are calculated as:

• Moles = 0.01 mol/L \( \times 0.1 \text{ L} = 0.001 \text{ moles} \)

This formula helps predict how substances will react and how much product will form in a reaction.

Avogadro's Number

Avogadro's number is an essential concept for chemists working with atoms and molecules. It lets you convert moles of a substance into the number of molecules or atoms. The number is approximately \(6.022 \times 10^{23}\), which signifies that one mole of any substance contains exactly this many molecules or atoms.
To convert moles to molecules, follow this simple process:

• Number of molecules = \( \text{moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \)

If you have 0.001 moles of a substance, multiplying by Avogadro's number gives:

• Number of molecules = 0.001 \( \times 6.022 \times 10^{23} = 6.022 \times 10^{20} \text{ molecules}\)

This conversion is invaluable for understanding proportions in chemical reactions and quantitative analyses.